By T.A. Laursen (auth.), Peter Wriggers Professor Dr., Udo Nackenhorst Professor Dr. (eds.)
Contact mechanics used to be and is a vital department in mechanics which covers a wide box of theoretical, numerical and experimental investigations. during this rigorously edited ebook the reader will receive a cutting-edge review on formula, mathematical research and numerical resolution methods of touch difficulties. The contributions accrued during this quantity summarize the lectures offered throughout the 4th touch Mechanics overseas Symposium (CMIS) held in Hannover, Germany, 2005, by means of major scientists within the quarter of touch mechanics.
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Additional resources for Analysis and Simulation of Contact Problems
We propose here to introduce a new distribution of the mass with the same total mass, center of gravity and inertia momenta. This distribution of the mass is done so that there is no inertia for the contact nodes (similarly to what happens in the continuous case). We refer the reader to  for further details. We assume that the modiﬁed mass matrix is still denoted M such that Ni T M Nj = 0, ∀ i, j ∈ IC . Then, the two following results hold. Theorem 2. Problem (1) with the equivalent mass matrix is well posed and has a Lipschitz continuous solution.
Venant–Kirchhoﬀ material in the 3D case. In the left picture of Figure 1, a cross section of the problem deﬁnition is shown. The lower domain Ωm models a half-bowl which is ﬁxed at the outer boundary as shown in the left picture of Figure 1. Against this bowl, we press Mortar methods for contact problems 41 d h Ωs r ri ra Ωm Fig. 1. Left: problem deﬁnition; middle: cut through the distorted domains with the eﬀective von Mises stress on level 3; right: contact stress λh · n on level 3. the body modeled by the domain Ωs .
For each of the discrete elements in contact, the contact force is calculated as a gradient of the corresponding potential function. The ﬁeld of contact forces is therefore a conservative ﬁeld. Nodal forces are obtained by integrating the distributed contact force over the overlapping area. As individual discrete elements are discretised into ﬁnite elements, the potentials ϕc and ϕt are written as a sum of potentials associated with individual ﬁnite elements. By providing diﬀerent potentials theoretically any interaction law can be obtained.
Analysis and Simulation of Contact Problems by T.A. Laursen (auth.), Peter Wriggers Professor Dr., Udo Nackenhorst Professor Dr. (eds.)